The moving plane method and the uniqueness of high order elliptic equation with GJMS operator
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866910929809047552 |
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| author | Zhang, Shihong |
| author_facet | Zhang, Shihong |
| contents | In this paper, we study the following high order elliptic equation involving the GJMS operator:
\begin{align*}
αP_{\mathbb{S}^n}v_α+2Q_{g_{\mathbb{S}^n}}=2Q_{g_{\mathbb{S}^n}}e^{nv_α}.
\end{align*}
We establish that if
$α>1$ and $n\geq3$, or if $α\in (1-ε_0, 1)$ with $n=2m\geq4$, then $v_α\equiv0$. As an application, we present a new proof of the classical Beckner inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_13119 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The moving plane method and the uniqueness of high order elliptic equation with GJMS operator Zhang, Shihong Analysis of PDEs 35A23, 35J60, 35B33, 35B38 In this paper, we study the following high order elliptic equation involving the GJMS operator: \begin{align*} αP_{\mathbb{S}^n}v_α+2Q_{g_{\mathbb{S}^n}}=2Q_{g_{\mathbb{S}^n}}e^{nv_α}. \end{align*} We establish that if $α>1$ and $n\geq3$, or if $α\in (1-ε_0, 1)$ with $n=2m\geq4$, then $v_α\equiv0$. As an application, we present a new proof of the classical Beckner inequality. |
| title | The moving plane method and the uniqueness of high order elliptic equation with GJMS operator |
| topic | Analysis of PDEs 35A23, 35J60, 35B33, 35B38 |
| url | https://arxiv.org/abs/2208.13119 |